"Once we got the physical squared away, there was no question he was going to become a Giant," said general manager Brian Sabean, who credited the pitcher for his swift decision.
Hudson made his major league debut with the Athletics in 1999 and went 92-39 in six seasons with Oakland, where the right-hander teamed with Mark Mulder and Barry Zito to form a successful "Big Three."
The 38-year-old went 8-7 with a 3.97 ERA in 21 starts this season for Atlanta. His season was cut short by a broken right ankle that required surgery. The Braves earlier this month declined to make a qualifying offer to Hudson, who won 49 games during the previous three seasons.
Hudson was hurt July 24 in New York when the Mets' Eric Young Jr. inadvertently stepped on the back of the pitcher's lower right leg while Hudson covered first base.
While he hasn't begun running on the ankle yet, he had a screw removed last week and expects to be full strength for spring training.
"The ankle's coming along just fine, not quite 100 percent right now but it's well on its way," he said. "I anticipate in the next month or so start throwing bullpens."
San Francisco, which missed the playoffs this year, is seeking another starter to join Matt Cain, Madison Bumgarner and Tim Lincecum in a rotation losing Zito and probably also free-agent righty Ryan Vogelsong.
Cain and Bumgarner are signed long term, while Lincecum received a $35 million, two-year deal last month.
"They have a ton of talent here, I was excited to join this rotation," Hudson said. "They're really good. They probably don't need my help."
Hudson was drafted by the A's in the sixth round of the 1997 amateur draft out of Auburn.
Oakland traded Hudson to the Braves in December 2004 and he pitched nine seasons in Atlanta. The three-time All-Star earned NL Comeback Player of the Year honors in 2010 after he returned from elbow ligament replacement surgery to go 17-9 with a 2.83 ERA. He had surgery for a herniated disk in November 2011.
The Giants had been eager to find an experienced starter to fill in the rotation. Zito just finished a $126 million, seven-year contract and had his $18 million option declined. Vogelsong's $6.5 million option also was turned down by the club.
"Great news with the need that we have for pitching here and to get Tim, who was one of the highly sought pitchers out there. I couldn't be more thrilled," manager Bruce Bochy said. "It certainly helps fill a very important need for us as we try to get back on track here. ... For him to choose us, we're honored and I look very forward to working with him."
Hudson traded text messages with good friend Zito on Monday — and now is filling a rotation spot vacated by Zito's departure.
"It's a bit odd," Hudson said. "We go back a long way. We were texting a little bit yesterday. He's happy for me and my family but it's a little bittersweet. I texted him I wish he'd been here with me. The game is what it is. Chapters open and close. I wish him the best."